Actually...I thought about how to avoid parity issues on the 4x4 and I realized that although there really is only permutation parity, with redux it seems like 2 different parities.
I dealt with the orientation parity by using ZZ. by pairing the edges and placing them oriented on the sides (using M freeslice) you could guarentee that those edges were oriented. After solving the EOline there are only 4 edges left to pair, which can be done in 2-3 algs.
Then I had to worry about the "PLL parity". I found that if the blocks were solved ZZ style and the corners done with COLL, the LL edges can be solved with parity, with only 5 more algs (1 being the standard PLL parity alg).
This results in a 2LLL all of the time, compared to the possible 4LLL with Fridrich Redux, and has a significantly lower movecount (20 if I remember correctly) which is shorter than the OLL parity algorithm.
But, because I have left ZZ for Roux, ZZ blockbuilding and COLL won't be used by me again, so I abandoned this idea, very well knowing that it could be extremely fast, faster than K4 even (don't say I didn't warn you Kir).